laura cui
@reionize.bsky.social
phd student @ caltech | interested in quantum info, math education, watercolors, marine bio
https://reionize.github.io
https://reionize.github.io
However, when this constraint is relaxed, we show it is possible to construct ensembles of quasi-local time-independent Hamiltonians which generate pseudorandom dynamics!
These ensembles can also be efficiently simulated assuming the existence of quantum-secure OWFs 💻
7/8
These ensembles can also be efficiently simulated assuming the existence of quantum-secure OWFs 💻
7/8
October 10, 2025 at 2:11 AM
However, when this constraint is relaxed, we show it is possible to construct ensembles of quasi-local time-independent Hamiltonians which generate pseudorandom dynamics!
These ensembles can also be efficiently simulated assuming the existence of quantum-secure OWFs 💻
7/8
These ensembles can also be efficiently simulated assuming the existence of quantum-secure OWFs 💻
7/8
On the other hand, in [2] we consider time evolution dynamics when factoring in uncertainty in H 🤔
When the connectivity of the system is known, we show that the dynamics of any ensemble of local Hamiltonians, at any time scale, can be distinguished from a random unitary.
6/8
When the connectivity of the system is known, we show that the dynamics of any ensemble of local Hamiltonians, at any time scale, can be distinguished from a random unitary.
6/8
October 10, 2025 at 2:11 AM
On the other hand, in [2] we consider time evolution dynamics when factoring in uncertainty in H 🤔
When the connectivity of the system is known, we show that the dynamics of any ensemble of local Hamiltonians, at any time scale, can be distinguished from a random unitary.
6/8
When the connectivity of the system is known, we show that the dynamics of any ensemble of local Hamiltonians, at any time scale, can be distinguished from a random unitary.
6/8
To prove this, we construct Hamiltonians which embed arbitrary Turing machines.
Under standard cryptographic assumptions, there exist Hamiltonians whose long-time dynamics perform computations that are out of reach for (& can be distinguished from) any efficient circuit 🤖
5/8
Under standard cryptographic assumptions, there exist Hamiltonians whose long-time dynamics perform computations that are out of reach for (& can be distinguished from) any efficient circuit 🤖
5/8
October 10, 2025 at 2:11 AM
To prove this, we construct Hamiltonians which embed arbitrary Turing machines.
Under standard cryptographic assumptions, there exist Hamiltonians whose long-time dynamics perform computations that are out of reach for (& can be distinguished from) any efficient circuit 🤖
5/8
Under standard cryptographic assumptions, there exist Hamiltonians whose long-time dynamics perform computations that are out of reach for (& can be distinguished from) any efficient circuit 🤖
5/8
While some models admit energy-conserving PRUs, we show that in general no efficient construction exists even for local 1D spin chains ⛓️
Not only that, determining if there exist energy-conserving PRUs for a given family of local 1D Hamiltonians is in general undecidable!
4/8
Not only that, determining if there exist energy-conserving PRUs for a given family of local 1D Hamiltonians is in general undecidable!
4/8
October 10, 2025 at 2:11 AM
While some models admit energy-conserving PRUs, we show that in general no efficient construction exists even for local 1D spin chains ⛓️
Not only that, determining if there exist energy-conserving PRUs for a given family of local 1D Hamiltonians is in general undecidable!
4/8
Not only that, determining if there exist energy-conserving PRUs for a given family of local 1D Hamiltonians is in general undecidable!
4/8
When can we use random unitaries to (efficiently) model physical dynamics? 💻 ⚛️
Excited to share a couple of works with Liang Mao, Fernando Brandão, Robert Huang, Thomas Schuster in which we explore this question!
[1] arxiv.org/abs/2510.08448
[2] arxiv.org/abs/2510.08434
1/8
Excited to share a couple of works with Liang Mao, Fernando Brandão, Robert Huang, Thomas Schuster in which we explore this question!
[1] arxiv.org/abs/2510.08448
[2] arxiv.org/abs/2510.08434
1/8
October 10, 2025 at 2:11 AM
When can we use random unitaries to (efficiently) model physical dynamics? 💻 ⚛️
Excited to share a couple of works with Liang Mao, Fernando Brandão, Robert Huang, Thomas Schuster in which we explore this question!
[1] arxiv.org/abs/2510.08448
[2] arxiv.org/abs/2510.08434
1/8
Excited to share a couple of works with Liang Mao, Fernando Brandão, Robert Huang, Thomas Schuster in which we explore this question!
[1] arxiv.org/abs/2510.08448
[2] arxiv.org/abs/2510.08434
1/8
also according to wikipedia the record for solar cell efficiency performance in r&d testing is close to 48% which is crazy when you compare to photosynthesis (~5%) and ecological trophic levels (~10%)
July 14, 2025 at 6:10 PM
also according to wikipedia the record for solar cell efficiency performance in r&d testing is close to 48% which is crazy when you compare to photosynthesis (~5%) and ecological trophic levels (~10%)
Adding one more note which I missed from the magic-augmented Cliffords paper
July 10, 2025 at 11:48 AM
Adding one more note which I missed from the magic-augmented Cliffords paper
With all the recent progress on designs and random unitaries, you might wonder if it's possible to do even better than log k and log log n
We show that the answer is no, by proving a new lower bound for the circuit depth needed for additive error designs w/ any # of ancillas
6/8
We show that the answer is no, by proving a new lower bound for the circuit depth needed for additive error designs w/ any # of ancillas
6/8
July 9, 2025 at 4:13 AM
With all the recent progress on designs and random unitaries, you might wonder if it's possible to do even better than log k and log log n
We show that the answer is no, by proving a new lower bound for the circuit depth needed for additive error designs w/ any # of ancillas
6/8
We show that the answer is no, by proving a new lower bound for the circuit depth needed for additive error designs w/ any # of ancillas
6/8
We also introduce a new framework for analyzing experiments on k copies of a unitary w/ processing steps in b/w 🖥️
We call distinguishability in this model "measurable error"
As a bonus we give a short alternate proof of the existence of pseudorandom unitaries w/ our framework!
5/8
We call distinguishability in this model "measurable error"
As a bonus we give a short alternate proof of the existence of pseudorandom unitaries w/ our framework!
5/8
July 9, 2025 at 4:13 AM
We also introduce a new framework for analyzing experiments on k copies of a unitary w/ processing steps in b/w 🖥️
We call distinguishability in this model "measurable error"
As a bonus we give a short alternate proof of the existence of pseudorandom unitaries w/ our framework!
5/8
We call distinguishability in this model "measurable error"
As a bonus we give a short alternate proof of the existence of pseudorandom unitaries w/ our framework!
5/8
A key fact we use is that random unitary statistics look the same (w/ 1/exp error) if we restrict to input spaces w/ k distinct basis states
We project onto alternating local distinct subspaces on which the moments of our circuit are equal to those of fully random unitaries
4/8
We project onto alternating local distinct subspaces on which the moments of our circuit are equal to those of fully random unitaries
4/8
July 9, 2025 at 4:13 AM
A key fact we use is that random unitary statistics look the same (w/ 1/exp error) if we restrict to input spaces w/ k distinct basis states
We project onto alternating local distinct subspaces on which the moments of our circuit are equal to those of fully random unitaries
4/8
We project onto alternating local distinct subspaces on which the moments of our circuit are equal to those of fully random unitaries
4/8
Our work combines efficient classical functions which appear random for any k different inputs (inspired by the PFC ensemble) w/ ideas from gluing
We also swap permutations for *shuffling operators* based on the "nearly random" functions to bring our depth down to log k 🤠
2/8
We also swap permutations for *shuffling operators* based on the "nearly random" functions to bring our depth down to log k 🤠
2/8
July 9, 2025 at 4:13 AM
Our work combines efficient classical functions which appear random for any k different inputs (inspired by the PFC ensemble) w/ ideas from gluing
We also swap permutations for *shuffling operators* based on the "nearly random" functions to bring our depth down to log k 🤠
2/8
We also swap permutations for *shuffling operators* based on the "nearly random" functions to bring our depth down to log k 🤠
2/8
What is the min depth you need for a random unitary?
In this work w/ Tommy Schuster, @RobertHuangHY, Fernando Brandão (arxiv.org/abs/2507.06216) we glue random unitary blocks w/ only random phases on log n qubits (fns on log n bits) to get designs in d = log k log log n 🧩
1/8
In this work w/ Tommy Schuster, @RobertHuangHY, Fernando Brandão (arxiv.org/abs/2507.06216) we glue random unitary blocks w/ only random phases on log n qubits (fns on log n bits) to get designs in d = log k log log n 🧩
1/8
July 9, 2025 at 4:13 AM
What is the min depth you need for a random unitary?
In this work w/ Tommy Schuster, @RobertHuangHY, Fernando Brandão (arxiv.org/abs/2507.06216) we glue random unitary blocks w/ only random phases on log n qubits (fns on log n bits) to get designs in d = log k log log n 🧩
1/8
In this work w/ Tommy Schuster, @RobertHuangHY, Fernando Brandão (arxiv.org/abs/2507.06216) we glue random unitary blocks w/ only random phases on log n qubits (fns on log n bits) to get designs in d = log k log log n 🧩
1/8